cube(d)

description

                 
 

	A surprisingly interesting family of polytopes Hd defined by the
	inequalites -1 <= xi <= 1.  Finding the 
	largest volume simplex in d-cube is an ongoing project
	[128, 127] as is finding the smallest 
	possible triangulation [126]. 
	A skewed class of cubes  gave the first hard examples for
	the simplex method [78].
	Cubes are conjectured to maximize diameter for d-polytopes 
	with 2d facets [174, 166, 165].
	For any triangle-free polytope P, fk(P) >= fk(Hd) [145];
	this same inequality is conjectured to hold for centrally-symmetric 
	polytopes [169]. Finally, cubes
	are conjectured to maximize the number of 
	pairs of estranged vertices (i.e. not sharing a facet) 
	for simple d polytopes with 2d
	facets [146].

keywords

vertices>>facets, simple, triangle-free, facet-degenerate, centrally-symmetric, triangulation, zero-one, zonotope

uses

interval

dim

d

n_facets

2d

n_vertices

2^d

facets

ksum(H([-1,1]),d)

vertices

V([-1,1])^d